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A substantial amount of phenotypic diversity results from changes in gene expression levels and patterns. Understanding how the transcriptome evolves is therefore a key priority in identifying mechanisms of adaptive change. However, in contrast to powerful models of sequence evolution, we lack a consensus model of gene expression evolution. Furthermore, recent work has shown that many of the comparative approaches used to study gene expression are subject to biases that can lead to false signatures of selection. Here we first outline the main approaches for describing expression evolution and their inherent biases. Next, we bridge the gap between the fields of phylogenetic comparative methods and transcriptomics to reinforce the main pitfalls of inferring selection on expression patterns and use simulation studies to show that shifts in tissue composition can heavily bias inferences of selection. We close by …